You're talking about a specific engine, the General Electric's GE36 Unducted Fan.

As found on wikipedia : it has a novel direct drive arrangement, where the reduction gearbox is replaced by a low-speed seven-stage free turbine. The turbine rotors drive one propeller, while the other propeller is connected to the free turbine stators and rotates in the opposite direction. So, in effect, the power turbine has 14 stages.

I don't know if current efforts into unducted fans still use that concept.

New Technology is the name we give to stuff that doesn't work yet. Douglas Adams

The GE36 was (as far as I know) the only attempt to make an ungeared UDF. Only one engine was made as a concept demonstrator on a contract with NASA.

In principle it was a separate unit added on the back of an off the shelf GE F-404 engine from an F/A-18 Super Hornet fighter. It was used as gas generator to power the aft UDF unit.

The back unit first split the gas into a wide annular gas flow so the UDF turbines could get a proper moment arm to pull the fan blades at the rather low speed, not much over 1500 rpm.

The UDF unit had two turbines each with 7 stages. One was a quite normal turbine pulling one fan in one direction.

The other 7 stages turbine "replaced" the stator vanes. The turbine blades were mounted on their outer ends inside a "barrel" which rotated in the opposite direction and pulled the other fan.

Mechanically it was an immensely complicated thing, and just the lubricating system was a nightmare to develop. How they also made variable pitch on all 16 fan blades is beyond me. But they did.

It had the potential to produce a more lightweight unit with high efficiency by eliminating the gearbox, and by eliminating the drag from separate stator vanes.

The single GE36 was optimized for speeds up to Mach 0.72, and a reviced version good for Mach 0.80 was planned.

The project was discontinued due to noise related problems.

The front fan on the Mach 0.72 version would be largely subsonic, but due to the accelerated air by the front fan the aft fan tips were supersonic. On a Mach 0.80 version the supersonic noise would have been somewhat more of a problem.

Always keep your number of landings equal to your number of take-offs, Preben Norholm

Current studies on open rotors are looking at both geared and ungeared configurations.

The GE36 met all its goals for performance. At the time it was expected that fuel prices would continue to rise and that fuel burn reduction would be a huge incentive to produce new aircraft with this configuration. But that did not come to pass. The main reason for dropping the program was the lack of a convincing cost-benefit trade in the face of low fuel price.

Since then the noise issues have been solved. Open rotor configurations are at the front of the pack for the next generation of narrow bodies (2025+).